Quadratic equation

Question

Samir drives600mi to Richmond averaging a certain speed. The return trip is made at an average speed that is 10 mph slower. Total time for the round trip is 22hr. Find Samir average speed on each part of the trip.

 

 

 

 

Answer 1

Distance = Rate x Time        Time = 600 / Rate      

 

600 = R x T       600 = (R - 10)(22 - T)         1200 = R x T + (R - 10)(22 - T)    

 

1200 = R (600/R) + (R - 10)(22 - 600/ R)      1200 = 600 + 22R -220 - 600 + 6000/R        

 

1200 = 22R - 220 + 6000/R  Multiply both sides by R    1200R = 22R^2 - 220R + 6000

 

Subtract 1200R from both sides   0 = 22R^2 - 1420R + 6000 = 2(11R^2 - 710R + 3000)= 2(11R-50)(R -60)

 

R = 60miles/ hour   T = 10 hours      R - 10 = 50     T = 12